Quantification of nuclear imaging and tomographic brain images acquired with the use of injected contrast agents, or tracers, require measurement of tracer blood concentration over the course of the scan. The blood concentration curve is used to account for metabolism, clearance and availability of the tracer to diffuse in the brain. Typically sampling is done via an arterial catheter, a procedure which is costly, risky to patients, time consuming, requires specialist, as well as expensive and error prone blood chemistry analysis. While some techniques exist that reduce number of required blood samples from 20 down to 1-3 for some tracers. The requirement of blood sampling limits clinical utility of many research tracers—it is not feasible to conduct tracer blood analysis in a clinic. Also, many research centers cannot conduct fully quantitative studies using many of the available tracers due to the added expense of blood sampling and analysis. There is a need for methods that are totally non-invasive (i.e. zero blood samples). This invention addresses this need. Iterative reconstruction with point spread function (PSF) modeling improves contrast recovery in positron emission tomography (PET) images, but also introduces ringing artifacts and over enhancement that is contrast and object size dependent. There is a need for mitigating these artifacts. The methods described herein address this need.